There are several things can cause an older belt drive turntable to run slowly or take a long time to come up to speed.

1. The belt has stretched or has become 'glazed'. If it is stretched, it will need to be replaced; that can be determined by how loose it is on the motor pulley.. If it has become 'glazed', it may benefit from a good cleaning with soap and water and a cotton rag.

2. The turntable main bearings lubrication have become dried out. It can become almost as thick and hard as molasses. This will require the use of a good solvent to clean out the bearing well via some cotton swabs. After it is totally clean, then re-lubricate the platter shaft very lightly with clock or sewing machine oil (5W or lower). Do not use motor oil or 3 in 1* oil as they are either too heavy or tend to dry out over time in my experience.

3. The motor bearing themselves may benefit from a tiny drop of clock oil (in many cases, only the top bearing is accessible). Be very careful not to use too much oil. I dip the tip of a toothpick into a little clock oil and then touch it to the motor shaft where it meets the plain bearing. If any oil gets on the pulley, be sure to clean it thoroughly before re-assembling the machine.

Those are the dominant things that I have discovered over time about belt drive turntables and their speed failures.

*3 in 1 oil seems to congeal for some reason after about three years slowing down the turntable again. 5W Clock oil does not seem to do that as readily.